The logic followed here is:

Hence, the correct answer is "Option 4".

The Correct answer is Ctrl + Spacebar.

Key Points

• Ctrl + Spacebar is the shortcut used in MS Word 365 to remove manual character formatting from selected text.
• This action restores the selected text to the default formatting applied by the paragraph style.
• Manual character formatting includes font styles, font sizes, bold, italic, underline, and other direct formatting changes.
• Using this shortcut ensures that the selected text adheres to the consistent formatting of the overall document.
• MS Word 365 provides various shortcuts to streamline formatting tasks, enhancing user productivity.
• This shortcut is particularly useful in situations where the text has been formatted inconsistently or requires a uniform style for professional appearance.
• Ctrl + Spacebar is supported across different versions of Microsoft Word, making it a universal formatting tool for users.

Additional Information

• Ctrl + Shift + N
• Ctrl + Shift + N is used to apply the Normal style to the selected text in MS Word.
• The Normal style is the default paragraph style for new documents and includes predefined font and spacing settings.
• This shortcut is different from Ctrl + Spacebar, as it applies a style rather than removing manual character formatting.
• Ctrl + Z
• Ctrl + Z is the shortcut for the Undo
• It reverses the last action performed by the user, whether it is text editing, formatting, or other changes.
• This shortcut does not remove character formatting but instead undoes recent modifications.
• Ctrl + B
• Ctrl + B is used to apply or remove bold formatting to the selected text.
• This shortcut is specific to bold styling and does not remove other manual formatting changes.
• It is commonly used for emphasizing text in documents.

The Correct answer is The file is moved to a special directory, and its directory entry is updated, but the data remains on the storage device.

Key Points

• When a file is moved to the 'Trash' or 'Recycle Bin' in a GUI-based Operating System, it is not permanently deleted.
• The file’s directory entry is updated to reflect its new location in a special directory (e.g., the Trash or Recycle Bin folder).
• The actual data remains on the storage device until the file is permanently deleted or the storage space is overwritten.
• This mechanism allows users to recover deleted files easily if they change their minds or deleted the file by mistake.
• The Trash or Recycle Bin acts as a , ensuring the file is not lost immediately and providing an opportunity for restoration.
• This functionality is common in operating systems like Windows, macOS, and Linux GUIs, making file management more user-friendly and less prone to accidental data loss.
• Files in the Trash or Recycle Bin typically still occupy storage space until they are permanently deleted or the Trash/Recycle Bin is emptied.

Additional Information

• The file’s data is immediately overwritten and unrecoverable.
• This is incorrect because simply moving a file to the Trash or Recycle Bin does not overwrite the data. Overwriting occurs only when specific tools or processes overwrite the storage sectors.
• Overwriting makes data recovery nearly impossible, but this is not the default behavior of the Trash/Recycle Bin feature.
• The file’s metadata (inode or equivalent) is immediately purged from the file system.
• When a file is moved to the Trash or Recycle Bin, its metadata is not purged immediately. Instead, its location is updated, and the metadata is preserved for potential recovery.
• Metadata purging occurs during permanent deletion or when the file system explicitly removes all references to the file.
• The file is compressed and archived before being permanently deleted.
• Trash/Recycle Bin does not compress or archive files by default. Files retain their original format and size while in the Trash/Recycle Bin.
• Compression is a separate process, often used in backup solutions, not for managing deleted files in most operating systems.

The correct answer is Africa-India Key Maritime Engagement.

Key Points

• The Africa-India Key Maritime Engagement was held in March 2025, marking the inaugural edition of this naval exercise.
• This exercise was specifically aimed at enhancing maritime cooperation between India and African nations.
• It reflects India’s ongoing efforts to strengthen security partnerships in the Indian Ocean Region (IOR) and bolster ties with African countries.
• The initiative is part of India’s strategy to ensure maritime security and promote a free, open, and inclusive Indo-Pacific region.
• It also underscores India’s commitment to fostering blue economy growth and addressing shared challenges such as piracy, illegal fishing, and climate change.
• This exercise is a significant step in India’s Act East Policy and its outreach towards African nations through maritime diplomacy.
• Participants included naval forces from several African coastal countries, showcasing a spirit of partnership and cooperation.

Additional Information

• Exercise MILAN
• Exercise MILAN is a biennial multilateral naval exercise hosted by the Indian Navy.
• It focuses on enhancing interoperability and maritime cooperation among participating nations.
• It is held in the Andaman and Nicobar Islands or the Eastern Naval Command in Visakhapatnam.
• The exercise involves activities such as maritime maneuvers, professional interactions, and cultural exchanges.
• Indian Ocean Naval Symposium (IONS)
• IONS is a voluntary initiative launched by the Indian Navy in 2008.
• It aims to enhance maritime cooperation among the littoral states of the Indian Ocean Region (IOR).
• IONS fosters discussions on topics like maritime security, disaster response, and sustainability.
• It includes member nations from South Asia, West Asia, East Africa, and Southeast Asia.
• Exercise VARUNA
• Exercise VARUNA is an annual bilateral naval exercise between India and France.
• It focuses on enhancing interoperability and strategic cooperation between the two nations’ navies.
• The exercise includes activities such as anti-submarine warfare, surface combat, and air defense drills.
• It underscores the strong defense partnership between India and France.

The logic followed here is,

Hence, the correct answer is "Option 3".

Given: M, N, O, P, Y and Z live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6.

Let's deduce the positions step by step:

1) N lives on the lowermost floor.

2) Only two people live between N and Z.

3) Only M lives above P. This means M is immediately above P.

4) Y lives on an even numbered floor.

<br>

The only person left is O, and the only floor left is Floor 3.

O is on Floor 3 and M is on Floor 6.

There are 2 people living between O and M.

Hence, the correct answer is "Option 1".

Given, 

Prabin starts from Point A and drives 12 km towards west.

He then takes a right turn, drives 8 km, turns right, and drives 14 km.

He then takes a right turn and drives 12 km.

He takes a final right turn, drives 2 km, and stops at Point P.

Therefore, he should drive 4 km towards the North to reach Point A again.

Hence, the correct answer is "Option 3".

Shortcut Trick

Ratio of student counts in Section A and Section B = 22 : 44 = 1 : 2.

Using the ratio method for weighted average: [(1 × 40) + (2 × 34)] ÷ (1 + 2).

Combined average weight = (40 + 68) ÷ 3 = 108 ÷ 3 = 36 kg.

∴ The correct answer is 36 kg.

Alternate Method

Given:

Students in Section A (n₁) = 22 | Average weight (x₁) = 40 kg

Students in Section B (n₂) = 44 | Average weight (x₂) = 34 kg

Formula Used:

Average weight of the class = (Sum of weights of all students) ÷ (Total number of students)

⇒ Total weight of Section A = 22 × 40 = 880 kg ⇒ Total weight of Section B = 44 × 34 = 1496 kg ⇒ Total class weight = 880 + 1496 = 2376 kg ⇒ Total class strength = 22 + 44 = 66 ⇒ Average weight of the whole class = 2376 ÷ 66 = 36 kg

∴ The correct answer is 36 kg.

Additional Information

Weighted Average Formula

When two groups are combined, the total average is calculated as (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Ratio Simplification

For average weight or score calculations, you can replace actual quantities with their simplest ratio to reduce numerical complexity.

Deviation Method

Pick an assumed average and calculate the net deviation. The final average is Assumed Average + (Net Deviation ÷ Total Count).

Shortcut Trick

When Distance is constant, Speed is inversely proportional to Time.

Speed ratio = 5 : 2 → Time ratio = 2 : 5.

Difference in time units = 5 − 2 = 3 units.

Given 3 units = 48 minutes ⇒ 1 unit = 16 minutes.

Usual time = 2 units = 2 × 16 = 32 minutes.

∴ The correct answer is 32 min.

Alternate Method

Given: New speed = 2/5 of Normal speed. Delay = 48 minutes.

Formula: Usual Time = [Late time × Numerator] ÷ [Denominator − Numerator]

⇒ Let normal speed be S and usual time be T.

⇒ New speed = (2/5) × S

⇒ Since Distance = Speed × Time, S × T = (2/5)S × (T + 48)

⇒ T = (2/5) × (T + 48)

⇒ 5T = 2T + 96

⇒ 3T = 96

⇒ T = 32 minutes

∴ The correct answer is 32 min.

Additional Information

Inverse Relationship of Speed and Time

If distance is constant, Speed₁/Speed₂ = Time₂/Time₁. This is the foundation for solving constant distance problems.

Direct Shortcut for Late/Early Problems

If a person travels at a/b of their usual speed and is 'L' minutes late, Usual Time = (a × L) ÷ |b − a|.

Average Speed for Constant Distance

When a person travels to a destination and back at speeds x and y, Average Speed = 2xy ÷ (x + y).

Given:

Simplify: (36)/(9) × (74 + 12) + 99

Formula used:

Basic arithmetic operations: Division, Multiplication, Addition

Calculation:

⇒ (36 ÷ 9) × (74 + 12) + 99

⇒ 4 × (74 + 12) + 99

⇒ 4 × 86 + 99

⇒ 344 + 99

⇒ 443

∴ The correct answer is option (3).

Shortcut Trick

Speed ratio = 5 : 2 (Normal : New)

Time ratio = 2 : 5 (Normal : New) [Since Distance is constant, Speed ∝ 1/Time]

Difference in time ratio = 5 − 2 = 3 units

Given 3 units = 18 minutes ⇒ 1 unit = 6 minutes

Usual time = 2 units = 2 × 6 = 12 minutes

∴ The correct answer is 12 min.

Alternate Method

Given:

New speed = 2/5 × Normal Speed

Time delay = 18 minutes

Formula Used:

Distance = Speed × Time

If distance is constant, s₁t₁ = s₂t₂

Calculations:

Let the usual speed be s and usual time be t.

⇒ Distance (D) = s × t

⇒ New speed = 2/5s

⇒ New time = t + 18

⇒ s × t = (2/5)s × (t + 18)

⇒ t = 2/5(t + 18)

⇒ 5t = 2t + 36

⇒ 3t = 36

⇒ t = 12 minutes

∴ The correct answer is 12 min.

Additional Information

Inverse Variation of Speed and Time

When the distance is constant, the time taken is inversely proportional to the speed (t ∝ 1/s).

Direct Formula for Late/Early

Usual Time = [Late time × (Ratio Numerator)] ÷ [Difference between Numerator and Denominator].

Average Speed

Average speed = (Total Distance) ÷ (Total Time). For two equal distances with speeds x and y, Average Speed = 2xy/(x + y).

The Correct answer is 0.024.

Key Points

• The unemployment rate for persons aged 15 years and above in rural India during the period 2022-23 was 2.4% (0.024).
• This data was reported in the Periodic Labour Force Survey (PLFS) Annual Report 2022-23, which is conducted by the National Statistical Office (NSO) under the Ministry of Statistics and Programme Implementation (MoSPI).
• The unemployment rate is calculated as the percentage of unemployed persons in the labor force (both employed and unemployed) during the reference period.
• The rural unemployment rate is generally lower than the urban unemployment rate due to the availability of agriculture-based employment in rural areas.
• The PLFS aims to provide reliable estimates of the labour force indicators, such as employment, unemployment, and labor participation rates, across rural and urban regions of India.
• This report helps the government and policymakers to frame employment and labor policies to address the challenges of unemployment in India.

Additional Information

• Importance of the PLFS:
• The PLFS is a significant survey for understanding the employment dynamics in India.
• It provides data on labor force participation rate (LFPR), worker population ratio (WPR), and unemployment rate (UR).
• The survey is conducted on a quarterly basis for urban areas and an annual basis for rural and urban combined estimates.
• Rural Employment in India:
• Agriculture remains the primary source of employment in rural India, employing a large percentage of the rural workforce.
• Other significant employment sectors in rural areas include construction, manufacturing, and services.
• Government programs like Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) play a crucial role in providing employment in rural regions.
• Unemployment Trends:
• The unemployment rate in rural areas is lower due to the prevalence of informal and seasonal employment.
• However, issues like underemployment and disguised unemployment are common in rural areas.

Shortcut Trick

For concentric circles, the length of the chord of the larger circle that is tangent to the smaller circle is given by:

Length of chord = 2 × √(R² − r²)

Where R = 26 cm and r = 10 cm.

⇒ Length = 2 × √(26² − 10²) = 2 × √(676 − 100)

⇒ Length = 2 × √576 = 2 × 24 = 48 cm.

∴ The correct answer is 48 cm.

Alternate Method

Given:

Radius of the larger circle (R) = 26 cm

Radius of the smaller circle (r) = 10 cm

Formula Used:

In a right-angled triangle, Pythagoras theorem states: Hypotenuse² = Base² + Perpendicular²

Let the two concentric circles have a common center O.

Let AB be the chord of the larger circle which is tangent to the smaller circle at point M.

Since OM is the radius of the smaller circle and AB is the tangent, OM ⊥ AB.

⇒ In right-angled ▵OMA, OA = 26 cm (Radius of larger circle) and OM = 10 cm (Radius of smaller circle).

Using Pythagoras theorem in ▵OMA:

⇒ OA² = OM² + AM²

⇒ 26² = 10² + AM²

⇒ 676 = 100 + AM²

⇒ AM² = 676 − 100 = 576

⇒ AM = √576 = 24 cm

Since the perpendicular from the center to a chord bisects the chord:

⇒ AB = 2 × AM = 2 × 24 = 48 cm

∴ The correct answer is 48 cm.

Additional Information

Concentric Circles

Circles that share the same center but have different radii are called concentric circles.

Tangent-Radius Property

The radius of a circle is always perpendicular to the tangent at the point of contact (OM ⊥ AB).

Chord Bisector Theorem

A perpendicular drawn from the center of a circle to a chord bisects the chord into two equal parts.

Let's analyze the given triads:

For, HO-JQ-LN

JQ-LS-NP

 

Option 4: LS-NU-PR follows the same logic.

 

Therefore, Option 4 follows the same pattern.

Hence, the correct answer is Option (4).

Shortcut Trick

Ratio of shares is determined by the time difference: 14 − 13 = 1 year.

At 10% rate, the multiplying factor is (1 + 10/100) = 11/10.

Ratio of Varun's share : Ashish's share = (11/10)¹ : 1 = 11 : 10.

Total units = 11 + 10 = 21 units → ₹1,218.

Value of 1 unit = 1,218 ÷ 21 = ₹58.

Ashish's share = 10 units × 58 = ₹580.

∴ The correct answer is ₹580.

Alternate Method

Given:

Total Amount = ₹1,218

Rate (R) = 10% per annum

Time for Varun (T_v) = 13 years

Time for Ashish (T_a) = 14 years

Formula Used:

Amount (A) = P(1 + R/100)^T

Calculations:

⇒ Amount for Varun = Amount for Ashish

⇒ P_v(1 + 10/100)¹³ = P_a(1 + 10/100)¹⁴

⇒ P_v × (1.1)¹³ = P_a × (1.1)¹⁴

⇒ P_v / P_a = (1.1)¹⁴ ÷ (1.1)¹³

⇒ P_v / P_a = 1.1 = 11 / 10

⇒ Ratio of shares P_v : P_a = 11 : 10

⇒ Ashish's share = [10 ÷ (11 + 10)] × 1,218

⇒ Ashish's share = (10 ÷ 21) × 1,218

⇒ Ashish's share = 10 × 58 = 580

∴ The correct answer is ₹580.

Additional Information

Compound Interest Amount Formula

The total amount A after n years is given by A = P(1 + r/100)ⁿ, where P is the principal and r is the annual interest rate.

Ratio of Principals for Equal Amounts

If amounts are equal after T₁ and T₂ years, the ratio of principals is P₁/P₂ = (1 + r/100)^{(T₂ − T₁)}.

Compound Interest (CI)

The interest earned is CI = A − P = P[(1 + r/100)ⁿ − 1].

Given Statements:

• Some guns are bombs.
• Some guns are cargos.
• Some bombs are riffles.

The least possible Venn diagram for the given statements is:

Conclusions:

I. Some guns are riffles. - False (There is no direct or indirect definite relationship established between "guns" and "riffles". Therefore, this conclusion does not logically follow.)

II. Some bombs are cargos. - False (There is no direct or indirect definite relationship established between "bombs" and "cargos". Therefore, this conclusion does not logically follow.)

So, Neither conclusion I nor II follows.

Hence, the correct answer is "Option 3".

The Correct answer is New Delhi.

Key Points

• New Delhi hosted the annual Conference of the International Institute of Administrative Sciences (IIAS) for the first time from 10-14 February 2025.
• The International Institute of Administrative Sciences (IIAS) is a global organization dedicated to the study and promotion of public administration and governance.
• India's hosting of this prestigious conference signifies its growing role in global administrative and governance discourses.
• New Delhi, the capital city of India, is known for its infrastructure and ability to host international conferences, summits, and events.
• The conference featured discussions on key topics related to public administration, policymaking, and global governance.
• New Delhi has been a hub for numerous international and diplomatic gatherings due to its strategic location and status as India's political capital.
• This event provided an opportunity for Indian policymakers and administrative professionals to interact and collaborate with global experts.
• Hosting the IIAS conference aligns with India’s efforts to showcase its advancements in administrative sciences and governance practices.

Additional Information

• Gandhinagar
• Gandhinagar, the capital city of Gujarat, is known for its planned city layout and administrative importance.
• It has hosted significant national events like Vibrant Gujarat Global Summit, which promotes investment and economic development.
• While Gandhinagar has modern infrastructure, it is not known for hosting international conferences like the IIAS meeting.
• Hyderabad
• Hyderabad, the capital of Telangana, is a major IT hub and known for its rich heritage.
• It has hosted events like Global Entrepreneurship Summit and UN Biodiversity Conference, showcasing its capability for international gatherings.
• However, the IIAS conference was not held in Hyderabad in 2025.
• Ahmedabad
• Ahmedabad, another prominent city in Gujarat, is known for its commercial significance and historic landmarks.
• It has hosted events like the World Heritage City Conference and Vibrant Gujarat but was not chosen for the IIAS conference.

The Correct answer is Designated Delhi as the National Capital Territory with a legislative assembly.

Key Points

• The Sixty-ninth Amendment Act, 1991 granted Delhi the status of a National Capital Territory (NCT).
• This amendment enabled Delhi to have its own legislative assembly and Council of Ministers to manage affairs related to certain subjects.
• It introduced Article 239AA into the Constitution of India, detailing the structure and functioning of the governance in Delhi.
• While Delhi was given a legislative assembly, it remained a Union Territory, with its legislative powers limited to specific domains like public order, police, and land under the control of the Union Government.
• Delhi's governance is unique as it has a blend of both the Union Government and a locally elected assembly, making it distinct from full-fledged states.
• The amendment aimed to strike a balance between Delhi's status as the capital city and granting it some degree of self-governance.
• The Chief Minister of Delhi is the head of the elected government, but the Lieutenant Governor retains significant powers and represents the Union Government.

Additional Information

• Brought Delhi under the control of the President through the Governor
• Delhi is governed by the Lieutenant Governor, who acts as the representative of the President of India, but it is not directly under the control of a Governor as seen in states.
• The Lieutenant Governor holds administrative authority and works alongside the elected government.
• Granted full Statehood to Delhi
• Delhi has not been granted full statehood. It remains a Union Territory with partial state-like governance powers.
• Matters like public order, police, and land are still under the control of the Union Government.
• Made Delhi a Union Territory without a legislature
• This option is incorrect because the Sixty-ninth Amendment Act explicitly provided Delhi with a legislative assembly to handle certain subjects.
• Delhi's governance model is distinct from a typical Union Territory without legislative powers, such as Chandigarh.

The logic followed here is,

Hence, the correct answer is "Option 2".

Shortcut Trick

Total cost of 20 dual desks = 20 × 3,500 = ₹70,000.

Total cost of 12 chairs = 79,600 − 70,000 = ₹9,600.

Average cost of a chair = 9,600 ÷ 12 = ₹800.

∴ The correct answer is ₹800.

Alternate Method

Given:

Total quantity: 20 desks and 12 chairs

Total combined cost: ₹79,600

Average cost per desk: ₹3,500

Formula Used:

Total Value = (Average Value × Number of Items)

Calculations:

⇒ Total cost of 20 desks = 20 × 3,500 = ₹70,000

⇒ Total cost of 12 chairs = Total bill − Total desk cost

⇒ Total cost of 12 chairs = 79,600 − 70,000 = ₹9,600

⇒ Average cost of a chair = Total chair cost ÷ Number of chairs

⇒ Average cost of a chair = 9,600 ÷ 12 = ₹800

∴ The correct answer is ₹800.

Additional Information

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the resulting average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Relationship between Total and Average

Sum of Observations = Average × Number of Observations. This is the fundamental rule used to find individual components from a total sum.

Mixture & Alligation

Average problems involving two distinct groups can also be solved using the alligation method to find the ratio of quantities or the missing average value.

Given:

$\left( \frac{21}{8} \right)^{12} \times \left( \frac{8}{21} \right)^{14} \times \left( \frac{21}{8} \right)^{14} = \left( \frac{8}{21} \right)^{9m + 20}$

Formula used:

$a^m \times a^n = a^{m+n}$

$\left( \frac{a}{b} \right)^n = \left( \frac{b}{a} \right)^{-n}$

Calculation:

LHS: $\left( \frac{21}{8} \right)^{12} \times \left( \frac{8}{21} \right)^{14} \times \left( \frac{21}{8} \right)^{14}$

⇒ $\left( \frac{21}{8} \right)^{12 + 14} \times \left( \frac{8}{21} \right)^{14}$

⇒ $\left( \frac{21}{8} \right)^{26} \times \left( \frac{21}{8} \right)^{-14}$

⇒ $\left( \frac{21}{8} \right)^{26 - 14}$ = $\left( \frac{21}{8} \right)^{12}$

Now express all powers in base $\left( \frac{8}{21} \right)$:

⇒  $\left( \frac{21}{8} \right)^{12}$ = $\left( \frac{8}{21} \right)^{-12}$

RHS = $\left( \frac{8}{21} \right)^{9m + 20}$

Now equating powers:

⇒ −12 = 9m + 20

⇒ 9m = −32

⇒ m = −32/9 

∴ The value of m is −$\frac{32}{9}$

The Correct answer is Goods and Services Tax.

Key Points

• Goods and Services Tax (GST) is an indirect tax implemented in India on July 1, 2017.
• It is a comprehensive, multi-stage, destination-based tax that is levied on every value addition.
• GST replaced multiple indirect taxes like Central Excise Duty, Service Tax, VAT, and others.
• It is governed by the Goods and Services Tax Act, 2017, and is categorized into Central GST (CGST), State GST (SGST), and Integrated GST (IGST).
• GST ensures a uniform tax structure across the country and eliminates the cascading effect of taxes.
• Under GST, consumers pay tax only on the value added to goods or services.
• It is implemented under the constitutional framework of Article 246A of the Indian Constitution, which grants powers to both the Parliament and State Legislatures to make laws regarding GST.
• GST applies to goods and services at different rates: 0%, 5%, 18%, and 40%, depending on the category.
• The introduction of GST has simplified the taxation system, promoted ease of doing business, and enhanced tax compliance.

Additional Information

• Equalisation Levy
• The Equalisation Levy, also known as the Google Tax, was introduced in India in 2016 to tax digital transactions.
• It aims to address taxation challenges posed by the digital economy, specifically targeting companies like Google, Facebook, and other online platforms.
• The levy is not considered a broad-based indirect tax like GST but is a targeted tax primarily applied to non-resident companies providing online advertising services.
• Capital Gain Tax
• Capital Gain Tax is a direct tax levied on the profit earned from the sale of a capital asset, such as property, stocks, or bonds.
• It is categorized into short-term capital gains and long-term capital gains based on the holding period of the asset.
• This tax is not an indirect tax and is paid directly by the individual or entity earning the profit.
• Corporate Tax
• Corporate Tax is a direct tax imposed on the income or profit of corporations and companies.
• It is calculated on the net income after expenses and deductions as per the Income Tax Act, 1961.
• Corporate Tax rates vary based on the type of company, such as domestic or foreign, and its turnover.

Conditions:

(i) If the first element is a symbol and the last a number, the codes for these two (the first and the last elements) are to be interchanged.

(ii) If the first element is an odd number and the last an even number, the first and last elements are to be coded as ©.

(iii) If both the second and third elements are perfect squares, the third element is to be coded as the code for the second element.

Given- 7 & 2 @ 9 % 2

Let's analyze the given group of numbers/symbols and the conditions:

• The first element is 7 (an odd number).
• The last element is 2 (an even number).
• The second element is & (a symbol, not a perfect square).
• The third element is 2 (not a perfect square).

Now let's check which conditions apply:

Rule No. (i): This condition does not apply because the first element (7) is a number, not a symbol.

Rule No. (ii): This condition applies because the first element (7) is an odd number and the last element (2) is an even number. So, the first and last elements will be coded as ©.

Rule No. (iii): This condition does not apply because neither the second element (&) nor the third element (2) are perfect squares.

Based on the applicable rule (ii), the first and last elements are coded as ©.

Now, let's find the codes for the remaining elements from the table:

• The code for & is M.
• The code for 2 is C.
• The code for @ is Z.
• The code for 9 is L.
• The code for % is P.

Thus, '7 & 2 @ 9 % 2' is coded as → © M C Z L P ©.

Hence, the correct answer is "Option 4".

Given A, B, C, D, G, H, and I are sitting around a circular table facing the centre.

Only one person sits between H and I when counted from the right of H.

Only one person sits between I and C.

Only one person sits between H and G.

Only two people sit between A and C.

Only one person sits between B and G.

And D sits at the remaining place.

"I" sits third to the right of D.

Hence, the correct answer is "Option 2".

Shortcut Trick

Total Interest earned = ₹2,100 − ₹1,680 = ₹420

Interest for 1 year = 4% of ₹1,680 = 16.8 × 4 = ₹67.2

Number of years (T) = Total Interest ÷ Interest per year

⇒ T = 420 ÷ 67.2 = 6.25 years

∴ The correct answer is 6.25 years.

Alternate Method

Given: Principal (P) = ₹1,680, Amount (A) = ₹2,100, Rate (R) = 4% per annum.

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100; Amount (A) = P + SI

⇒ SI = A − P = 2100 − 1680 = ₹420

⇒ 420 = (1680 × 4 × T) ÷ 100

⇒ 420 × 100 = 6720 × T

⇒ 42000 = 6720 × T

⇒ T = 4200 ÷ 672

⇒ T = 6.25 years

∴ The correct answer is 6.25 years.

Additional Information

Simple Interest (SI)

It is calculated only on the initial Principal amount. Formula: SI = (P × R × T) ÷ 100.

Amount in Simple Interest

The total money returned after a period is A = P × [1 + (R × T) ÷ 100].

Rate of Interest

If Time and Principal are constant, Simple Interest is directly proportional to the Rate of Interest.

The Correct answer is ₹8,000 crore.

Key Points

• The Smart City Mission is a flagship program launched by the Government of India in 2015.
• The mission aims to promote core infrastructure, sustainable urban development, and a better quality of life for citizens.
• The budget allocated for the financial year 2023-24 under the Smart City Mission is ₹8,000 crore.
• This fund is utilized for developing 100 smart cities across India with focus on smart solutions like better urban mobility, improved sanitation, and efficient energy use.
• Under the mission, cities aim to use technology, governance, and innovation to address urban challenges.
• Projects funded include integrated command and control centers, waste management systems, and smart transportation networks.
• The Smart City Mission is coordinated by the Ministry of Housing and Urban Affairs, ensuring efficient utilization of funds.
• The mission aligns with broader goals like Sustainable Development Goals (SDGs) and India's commitment to urban transformation.

Additional Information

• ₹12,000 crore
• This option is incorrect as the allocated budget for the financial year 2023-24 under the Smart City Mission is ₹8,000 crore, not ₹12,000 crore.
• ₹12,000 crore could refer to allocations under other government missions or programs in different sectors.
• ₹6,000 crore
• The amount of ₹6,000 crore is lower than the actual allocation made for the Smart City Mission in 2023-24.
• This amount might correspond to other urban development programs or regional initiatives outside the scope of the mission.
• ₹10,000 crore
• ₹10,000 crore exceeds the budget allocated for the Smart City Mission in the financial year 2023-24.
• Although larger budgets have been allocated to urban development in India in the past, the mission-specific allocation remains at ₹8,000 crore.

The Correct answer is MS Swaminathan.

Key Points

• MS Swaminathan, often referred to as the Father of the Green Revolution in India, was the chairman of the National Commission on Farmers (NCF) when it was constituted on 18 November 2004.
• The primary focus of the NCF under his leadership was to address issues related to sustainable agriculture, food security, and the welfare of farmers.
• He played a pivotal role in introducing high-yielding varieties of wheat and rice to India, which significantly increased agricultural production in the country during the Green Revolution.
• MS Swaminathan has been a staunch advocate for the use of science and technology to improve agricultural productivity while ensuring the conservation of natural resources.
• The NCF under his leadership proposed several key recommendations, including the establishment of Farmer Welfare Fund and providing farmers access to resources like credit, seeds, and irrigation facilities.
• The commission emphasized the need for a pro-farmer policy framework to ensure that farmers' incomes are stabilized and enhanced.
• MS Swaminathan has also contributed significantly to the global agricultural research landscape and has been recognized with numerous awards, including the World Food Prize.

Additional Information

• Krishnaswamy Kasturirangan
• Krishnaswamy Kasturirangan is an eminent Indian scientist known for his contributions to space research.
• He served as the Chairman of ISRO (Indian Space Research Organisation) from 1994 to 2003.
• He has played a key role in India's space missions, including the development of the Indian Remote Sensing satellites and INSAT series.
• He was also involved in drafting the National Education Policy (NEP) 2020.
• Chakravarthi Rangarajan
• Chakravarthi Rangarajan is a renowned Indian economist and former Governor of the Reserve Bank of India (RBI).
• He has also served as the Chairman of the Economic Advisory Council to the Prime Minister.
• His work has focused on monetary policy, economic reforms, and financial stability.
• Verghese Kurien
• Verghese Kurien, known as the Father of the White Revolution in India, was instrumental in transforming India into the largest producer of milk in the world.
• He founded the Amul cooperative movement, which helped revolutionize India's dairy industry.
• He established the National Dairy Development Board (NDDB) and played a key role in implementing Operation Flood, one of the largest agricultural programs in India.

The Correct answer is 31.

Key Points

• As per the Indian Space Association (ISpA), by the year 2025, out of the approved 52-satellite constellation for the defence sector, 31 satellites are expected to be built by the private sector.
• This marks a significant step towards the involvement of private entities in the development of India's space and defence-related technologies.
• The initiative supports the vision of self-reliance (Atmanirbhar Bharat) in the space sector, as promoted by the Government of India.
• Private sector participation is crucial in reducing the burden on public organizations like the Indian Space Research Organisation (ISRO) and fostering innovation through competitive development.
• The 31 satellites are expected to cater to defence-related communication, surveillance, and strategic needs, strengthening India's national security infrastructure.
• This move aligns with the space sector reforms introduced in recent years, aiming to provide more opportunities to private players and startups in the space ecosystem.

Additional Information

• Private Sector Involvement in Space
• Recently, the Government of India has introduced policy reforms to facilitate private sector participation in the space sector.
• Organizations like IN-SPACe (Indian National Space Promotion and Authorization Center) have been established to promote and regulate private sector activities in space.
• Startups and private companies like Skyroot Aerospace, Agnikul Cosmos, and Pixxel have emerged as key players in India's evolving space industry.
• The government also aims to commercialize space technology through its commercial arm, NewSpace India Limited (NSIL).
• Defence Space Applications
• Satellites play a vital role in military communication, navigation, surveillance, and reconnaissance.
• They provide critical information for border security, disaster management, and strategic operations.
• Examples of defence-oriented satellites include RISAT (Radar Imaging Satellite) and GSAT series satellites.

The logic follows here is :-

Given numbers: 773 263 387 270 378

The lowest number is 263.

Now, extract the first digit of the lowest number:

• First digit of 263 is 2.

The highest number is 773.

Then, extract the first digit of the highest number:

• First digit of 773 is 7.

Finally, subtract the first digit of the lowest number from the first digit of the highest number:

Resultant = (First digit of highest number) - (First digit of lowest number)

Resultant = 7 - 2 = 5

Hence, the correct answer is "Option 1".

Given:

: UWC :: OHW : %

Option 1) # = KXS, % = SRA

For KXS to UWC:

Pattern for KXS to UWC: (+10, +3, +10)

For OHW to SRA 

The patterns (+10, +3, +10) and (+4, +11, +4) are not the same. So, Option 1 is incorrect.

Option 2) # = SRA, % = QMY

For SRA to UWC:

Pattern for SRA to UWC: (+2, +5, +2)

For OHW to QMY

Pattern for OHW to QMY: (+2, +5, +2).

This pattern matches the pattern for SRA to UWC!

Option 3) # = QMY, % = MCU

For QMY to UWC:

Pattern for QMY to UWC: (+4, +10, +4)

For OHW to MCU 

The patterns (+4, +10, +4) and (-2, -5, -2) are not the same. So, Option 3 is incorrect.

Option 4) # = MCU, % = KXS

For MCU to UWC:

Pattern for MCU to UWC: (+8, +20, +8)

For OHW to KXS

The patterns (+8, +20, +8) and (-4, +16, -4) are not the same. So, Option 4 is incorrect.

Hence, the correct answer is "Option 2".

The Correct answer is State Bank of India.

Key Points

• The State Bank of India (SBI) launched a unique product called ‘Asmita’ on International Women’s Day 2025.
• ‘Asmita’ is a collateral-free digital SME loan specifically designed for women entrepreneurs, aiming to support and empower them.
• The loan offers women an opportunity to scale their businesses without the burden of providing collateral, thus encouraging financial independence.
• The initiative aligns with the bank’s commitment to promoting gender inclusivity in the business and financial sector.
• State Bank of India is India's largest public sector bank, with a wide reach and extensive customer base.
• By introducing products like ‘Asmita,’ SBI demonstrates a focus on fostering women’s entrepreneurship and contributing to economic growth.
• This product is expected to benefit women across various industries, providing them a platform to access credit digitally without cumbersome paperwork.

Additional Information

• Bank of Baroda
• Bank of Baroda is one of the leading public sector banks in India.
• It was established in 1908 and is headquartered in Vadodara, Gujarat.
• The bank is known for its innovative financial products and has a strong international presence.
• While it offers loans for SMEs and women entrepreneurs, it did not launch the ‘Asmita’ loan on International Women’s Day 2025.
• HDFC Bank
• HDFC Bank is a leading private sector bank in India and is known for its superior technology-driven services.
• It was established in 1994 and is headquartered in Mumbai, Maharashtra.
• HDFC Bank offers a range of business loans and financial products; however, it was not the bank that launched the ‘Asmita’ loan.
• Axis Bank
• Axis Bank is another prominent private sector bank in India, established in 1993.
• Headquartered in Mumbai, it provides various SME loans and initiatives for women entrepreneurs.
• Although Axis Bank is known for its focus on women-centric initiatives, it was not the initiator of the ‘Asmita’ loan.

Shortcut Trick

Let the Cost Price (CP) of the manufacturer be x.

Successive selling price chain: x × 105/100 × 110/100 × 115/100 = 11,300.

x × 1.05 × 1.10 × 1.15 = 11,300.

x × 1.32825 = 11,300.

x = 11,300 ÷ 1.32825 = 8,507.4346...

∴ The correct answer is ₹8,507.43.

Alternate Method

Given → Retail Price = ₹11,300 | Manufacturer Profit = 5% | Wholesaler Profit = 10% | Retailer Profit = 15%. Formulas: SP = CP × (100 + P%)/100 | Final Price = Initial CP × (1 + r₁/100) × (1 + r₂/100) × (1 + r₃/100).

⇒ Let initial CP be CP. ⇒ Price after Manufacturer = CP × 1.05. ⇒ Price after Wholesaler = (CP × 1.05) × 1.10. ⇒ Price after Retailer = (CP × 1.05 × 1.10) × 1.15 = 11,300. ⇒ CP × 1.32825 = 11,300. ⇒ CP = 11,300 ÷ 1.32825 = 8,507.434... ∴ The correct answer is ₹8,507.43.

Additional Information

Successive Percentage Changes

When a value is increased by x%, y%, and z% successively, the final value is Initial × (1 + x/100) × (1 + y/100) × (1 + z/100).

Retailer and Customer

The Selling Price of one entity in the supply chain becomes the Cost Price for the next entity.

The Correct answer is AO Hume.

Key Points

• The 'Safety Valve Theory' is associated with AO Hume, a retired British civil servant who played a key role in the formation of the Indian National Congress (INC) in 1885.
• This theory suggests that the British government supported the establishment of the INC as a means to provide a platform for Indians to express their grievances peacefully, thus preventing revolutionary activities.
• AO Hume believed that by channeling Indian discontent into constitutional and non-violent methods, the British could maintain control over India while addressing some concerns.
• He was instrumental in bringing together prominent Indian leaders and intellectuals to form the INC, which later became a significant force in India's struggle for independence.
• The INC was initially meant to serve as a forum for educated Indians to discuss political issues and advise the British administration on reforms.
• The theory has been debated by historians, with some accepting its validity and others arguing that the INC was formed due to genuine political aspirations of Indian leaders rather than British motives.

Additional Information

• Lord Dufferin
• Lord Dufferin was the Viceroy of India from 1884 to 1888.
• Although he did not directly form the INC, he interacted with its leaders and played a role in facilitating its early discussions.
• He supported the idea of addressing Indian grievances, but his involvement was more indirect compared to AO Hume.
• WC Bannerji
• WC Bannerji was the first president of the Indian National Congress in 1885.
• He was a prominent lawyer and political leader known for his advocacy of constitutional reforms and moderate politics.
• While he played an important role in the INC's early leadership, the 'Safety Valve Theory' is not directly associated with him.
• Dadabhai Naoroji
• Dadabhai Naoroji was a key figure in Indian nationalism and the INC, often referred to as the Grand Old Man of India.
• He was known for his economic critique of British colonial rule, especially the 'Drain of Wealth' theory.
• Though he contributed significantly to the INC, his focus was more on economic issues rather than the 'Safety Valve Theory.'

Shortcut Trick

Total Work (LCM of 57, 28, 19) = 1596 units.

Efficiency of A = 1596 ÷ 57 = 28 units/hr.

Efficiency of A + C = 1596 ÷ 19 = 84 units/hr → Efficiency of C = 84 − 28 = 56 units/hr.

Efficiency of B + C = 1596 ÷ 28 = 57 units/hr → Efficiency of B = 57 − 56 = 1 unit/hr.

Time taken by B = 1596 ÷ 1 = 1596 hours.

∴ The correct answer is 1596 hours.

Alternate Method

Given:

Time taken by A = 57 hours

Time taken by B + C = 28 hours

Time taken by A + C = 19 hours

Formula Used:

Efficiency = Total Work ÷ Time

Calculations:

⇒ Efficiency of A = 28

⇒ Efficiency of A + C = 84

⇒ Efficiency of C = (A + C) − A = 84 − 28 = 56

⇒ Efficiency of B + C = 57

⇒ Efficiency of B = (B + C) − C = 57 − 56 = 1

⇒ Time taken by B alone = Total Work ÷ Efficiency of B

⇒ Time = 1596 ÷ 1 = 1596 hours

∴ The correct answer is 1596 hours.

Additional Information

Combined Efficiency

When multiple people work together, their individual efficiencies are added to find the total rate of work per unit time.

Total Work Assumption

Taking the LCM (Least Common Multiple) of the given time durations as the total work simplifies calculations by ensuring efficiencies are integers.

Inverse Relationship

For a constant amount of work, Time is inversely proportional to Efficiency (T ∝ 1/E).

The correct answer is Ctrl + O.

Key Points

• Ctrl + O is a universal shortcut used in several applications, including Microsoft PowerPoint, to open an existing file or presentation.
• This shortcut improves productivity by allowing users to access files quickly without navigating through menus manually.
• In the context of Microsoft PowerPoint, pressing Ctrl + O will directly open the "Open" dialog box, enabling users to browse and select a file to work on.
• It is part of the broader suite of keyboard shortcuts designed to enhance user efficiency within the Microsoft Office environment.
• The shortcut is widely recognized and standardized across various programs, making it a valuable tool for users familiar with Windows-based applications.
• Keyboard shortcuts like Ctrl + O reduce dependency on a mouse and are particularly beneficial for users aiming for speed and accuracy.

Additional Information

• Shift + O
• This combination does not perform any specific function in Microsoft PowerPoint.
• In some software, Shift may modify other shortcut keys, but it is not associated with opening presentations.
• Alt + O
• Alt + O is not a default shortcut for opening files in Microsoft PowerPoint.
• In older versions of Microsoft Word, this combination was used to open the "Format" menu, but it has no relevance in PowerPoint.
• Tab + O
• Tab is typically used for navigation purposes, such as moving between fields or options.
• It is not used in combination with O to open a file or presentation in PowerPoint.

The Correct Answer is Thailand.

In News

• Football: India secures AFC Women’s Asian Cup Qualification for the first time.

Key Points

• India beat Thailand 2–1 in their final AFC Women’s Asian Cup 2026 Qualifiers (Group B) match.
• The match was held at the 700th Anniversary of Chiang Mai Stadium in Thailand.
• Sangita Basfore scored a brace (2 goals) for India; Chatchawan Rodhong scored for Thailand.
• The match was a virtual playoff, as both teams had 9 points and an identical +22 goal difference.
• India qualified for the 2026 AFC Women’s Asian Cup, to be held in Australia.
• This is India’s first qualification in 22 years through regular competition (last time: 2003).
• India was automatically qualified in 2022 as hosts but had to withdraw due to a COVID-19 outbreak.

The logic follows here is :-

Given numbers: 898 740 280 169 993

The highest number is 993.

First digit of the highest number:

• First digit of 993 is 9.

The lowest number is 169.

Then, Third digit of the lowest number:

• Third digit of 169 is 9.

Finally, add the first digit of the highest number to the third digit of the lowest number:

Resultant = (First digit of highest number) + (Third digit of lowest number)

Resultant = 9 + 9

Resultant = 18

Hence, the correct answer is "Option 4".

Shortcut Trick

Arrange the given 11 observations in ascending order:

11, 32, 45, 53, 56, 79, 81, 87, 94, 98, 99

Since the number of terms (N = 11) is odd, the median is the exact middle term:

Median = ((11 + 1) ÷ 2)^th term = 6^th term = 79

∴ The correct answer is 79.

Alternate Method

Given:

Observations: 87, 56, 79, 81, 11, 53, 94, 45, 32, 99, 98

Total number of observations (N) = 11

Formula Used:

When N is odd, Median = ((N + 1) ÷ 2)^th term (after arranging in ascending order).

Calculations:

First, arrange the given observations in ascending order:

⇒ 11, 32, 45, 53, 56, 79, 81, 87, 94, 98, 99

Count the total number of observations:

⇒ N = 11

Since N is an odd number, the median is calculated as:

⇒ Median = ((N + 1) ÷ 2)^th term

⇒ Median = ((11 + 1) ÷ 2)^th term

⇒ Median = (12 ÷ 2)^th term

⇒ Median = 6^th term

Looking at the ordered list, the 6^th term is 79.

⇒ Median = 79

Option Analysis:

⇒ Option (1) 53: This is the 4^th term in the sorted list, not the middle term.

⇒ Option (2) 56: This is the 5^th term in the sorted list, which is just before the middle term.

⇒ Option (3) 81: This is the 7^th term in the sorted list, which is just after the middle term.

⇒ Option (4) 79: This is the exact 6^th (middle) term, which is the correct median.

∴ The correct answer is 79.

Additional Information

Median for Even Number of Terms

If the number of observations (N) is even, the median is the average of the (N ÷ 2)^th term and the ((N ÷ 2) + 1)^th term after arranging them in ascending order.

Relation between Mean, Median, and Mode

For a moderately skewed distribution, the empirical relationship is: Mode = 3 × Median − 2 × Mean.

Effect of Outliers on Median

Unlike the mean, the median is a robust measure of central tendency and is not heavily influenced by extremely large or small values (outliers).

Shortcut Trick

Use the relationship: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

MP ÷ CP = (100 + 68) ÷ (100 − 16) = 168 ÷ 84 = 2 ÷ 1.

Since MP is 2 and CP is 1, the markup is 1 unit over 1 unit of CP.

Markup percentage X = (1 ÷ 1) × 100 = 100%.

∴ The correct answer is 100.

Alternate Method

Given: Discount% = 16%, Profit% = 68%.

Formulas: SP = CP × (100 + P%) ÷ 100 | SP = MP × (100 − D%) ÷ 100 | MP = CP × (100 + X%) ÷ 100.

⇒ Let Cost Price (CP) be 100.

⇒ Selling Price (SP) = 100 + 68 = 168.

⇒ Since Discount is 16%, SP = 84% of Marked Price (MP).

⇒ 84% of MP = 168 ⇒ MP = (168 ÷ 84) × 100 = 200.

⇒ Markup Value = MP − CP = 200 − 100 = 100.

⇒ Markup Percentage (X) = (100 ÷ 100) × 100 = 100.

∴ The correct answer is 100.

Additional Information

Marked Price & Discount

Marked Price is the price printed on the label. Discount is always calculated on the Marked Price: SP = MP − Discount.

Relation between CP and MP

The direct ratio MP/CP = (100 + P%)/(100 − D%) is derived by equating the two SP formulas.

The logic followed in this pattern is based on alphabetical shifts between consecutive letters within each cluster.

For 'BEH':

For 'FHL':

For 'ACG':

For 'SUY':

All letter-clusters except 'BEH' follow the pattern of adding +2 to the first letter to get the second, and adding +4 to the second letter to get the third.

'BEH' follows a +3, +3 pattern.

Hence, the letter-cluster that DOES NOT belong to that group is "1) BEH".

Hence, the correct answer is "Option 1".

Given, Seven people, I, J, K, L, O, P and Q are sitting in a row, facing north.

No one sits to the right of I.

Only three people sit between I and J.

Only two people sit between J and Q.

L sits third to the left of P.

K sits to the immediate right of P.

Three people sit between O and Q.

Hence, the correct answer is "Option 1".

The Correct answer is Reservation for SC/ST in legislatures.

Key Points

• The 104th Constitutional Amendment Act, 2020 extended the provision for reservation of seats for Scheduled Castes (SC) and Scheduled Tribes (ST) in the Lok Sabha and State Legislative Assemblies.
• This reservation was originally provided under Article 334 of the Indian Constitution.
• Such reservations were introduced for a period of 70 years starting from the adoption of the Constitution in 1950.
• The amendment extended the reservation for SCs and STs by 10 years, thereby ensuring these provisions until 2030.
• The primary aim of this provision is to ensure adequate political representation for marginalized communities in legislative bodies.
• The reservation does not apply to seats in the Rajya Sabha and Legislative Councils, as these are indirectly elected bodies.
• It highlights India’s commitment to social justice and the inclusion of disadvantaged communities in the political process.

Additional Information

• Voting age for elections
• The voting age in India was reduced from 21 years to 18 years by the 61st Constitutional Amendment Act, 1988.
• This amendment aimed to provide greater political participation for the youth of India.
• The reduction of voting age applies to elections for the Lok Sabha and State Legislative Assemblies.
• GST Council term
• The GST Council was established under Article 279A of the Indian Constitution.
• It was introduced through the 101st Constitutional Amendment Act, 2016.
• The Council is responsible for making decisions related to Goods and Services Tax (GST).
• There is no specific term for the GST Council as it is a permanent body.
• Term of the Lok Sabha
• The term of the Lok Sabha is defined as five years under Article 83 of the Indian Constitution.
• The Lok Sabha can be dissolved earlier by the President on the advice of the Council of Ministers.
• The term can also be extended during a national emergency under provisions of Article 352.

The Correct answer is Madras.

Key Points

• V.O. Chidambaram Pillai, also known as "Kappalottiya Tamilan," was a prominent Indian freedom fighter and a key figure in the Swadeshi Movement.
• He was actively involved in the revolutionary movement in the region of Madras Presidency, which is now a part of modern-day Tamil Nadu.
• He was instrumental in establishing the first indigenous shipping service, the Swadeshi Steam Navigation Company, to compete with British shipping companies.
• V.O. Chidambaram Pillai was deeply influenced by the ideas of Bal Gangadhar Tilak and used his entrepreneurial skills to strengthen the Swadeshi Movement.
• He contributed significantly to the cause of economic independence by promoting indigenous industries and creating awareness about the exploitation by colonial powers.
• He was arrested by the British authorities in 1908 for his revolutionary activities and was subjected to rigorous imprisonment, including forced labor.
• His life and legacy remain an integral part of the history of the freedom struggle in the Madras region.

Additional Information

• Delhi
• Delhi was a significant center during India's freedom struggle, but it was more prominently associated with movements like the 1857 Revolt and the activities of revolutionaries such as Bhagat Singh and others during the later phases of the struggle.
• However, V.O. Chidambaram Pillai's revolutionary activities were not focused in Delhi.
• Bombay
• Bombay (now Mumbai) was the hub of many prominent leaders like Gopal Krishna Gokhale and Dadabhai Naoroji, and was central to the early phases of the Indian National Congress.
• Though Bombay played a major role in the freedom movement, V.O. Chidambaram Pillai’s contributions were focused in the Madras region.
• Calcutta
• Calcutta (now Kolkata) was the capital of British India until 1911 and a major center for revolutionary activities led by groups like the Anushilan Samiti and leaders such as Aurobindo Ghosh.
• While Calcutta was pivotal in shaping the freedom movement, V.O. Chidambaram Pillai's work was concentrated in Madras Presidency.

Shortcut Trick

Combine the ratios directly since the term b is already common with the same value 4.

Ratio a : b : c = 3 : 4 : 7.

Substitute these values directly into the expression: (3 + 4 + 7) ÷ 7 = 14 ÷ 7 = 2.

∴ The correct answer is 2.

Alternate Method

Given:

⇒ a : b = 3 : 4

⇒ b : c = 4 : 7

Formula Used:

⇒ If a : b = x : y and b : c = y : z, then a : b : c = x : y : z.

Calculations:

⇒ Since b is equal to 4 in both ratios, we can write:

⇒ a : b : c = 3 : 4 : 7

⇒ Let a = 3k, b = 4k, and c = 7k, where k is a constant.

⇒ Required expression = (a + b + c) ÷ c

⇒ Required expression = (3k + 4k + 7k) ÷ 7k

⇒ Required expression = 14k ÷ 7k

⇒ Required expression = 2

∴ The correct answer is 2.

Additional Information

Compound Ratio

For two or more ratios, if we multiply the antecedents together and the consequents together, the ratio so obtained is called their compound ratio. For a : b and c : d, the compound ratio is ac : bd.

Combining Ratios

To combine ratios a : b and b : c when the value of b is different, multiply the first ratio by the b-value of the second, and the second ratio by the b-value of the first to make the b-term common.

Homogeneous Expressions

In a fraction where the numerator and denominator are homogeneous expressions of the same degree, the actual constant 'k' cancels out, allowing direct substitution of ratio terms.

The logic followed here is based on alphabetical shifts within each cluster pair.

Let's analyze each option:

Option 1) GJ - PS:

Option 2) JM - SV:

Option 3) EH - NQ:

Option 4) MQ - UZ:

So, the letter-cluster pair that DOES NOT belong to that group is "4) MQ - UZ".

Hence, the correct answer is "Option 4".

Given series:

8 £ 6 @ & % 4 6 @ 8 $ 7 & 3 Ω 9 # 1 * 4 5

Condition to be checked:

The pattern we are looking for is: Even Number → Symbol → Odd Number

Let's go through the series from left to right and identify the symbols:

8 £ 6 @ & % 4 6 @ 8 $ 7 & 3 Ω 9 # 1 * 4 5

Thus, there is only one such pattern (8 $ 7) that follows the given condition.

Hence, the correct answer is "Option 3".

Shortcut Trick

Ratio of cost of Shirt (S) to Trouser (T) is 4 : 3 (since 3S = 4T).

Total units for 5 shirts and 7 trousers = (5 × 4) + (7 × 3) = 41 units.

Given 41 units = ₹6,150 ⇒ 1 unit = ₹150.

Required cost for 2 shirts and 2 trousers = 2 × (4 + 3) = 14 units.

Final Cost = 14 × 150 = ₹2,100.

∴ The correct answer is ₹2,100.

Alternate Method

Given:

Cost of 5 Shirts (S) + 7 Trousers (T) = ₹6,150

Cost of 3 Shirts = Cost of 4 Trousers ⇒ 3S = 4T

Calculations:

⇒ From 3S = 4T, we get S = 4T/3

⇒ Substitute S in the first equation: 5(4T/3) + 7T = 6150

⇒ (20T/3) + 7T = 6150

⇒ (20T + 21T) / 3 = 6150

⇒ 41T / 3 = 6150

⇒ 41T = 18450

⇒ T = 18450 ÷ 41 = ₹450

⇒ S = (4 × 450) ÷ 3 = ₹600

⇒ Cost of 2 shirts and 2 trousers = 2(600) + 2(450)

⇒ 1200 + 900 = ₹2,100

∴ The correct answer is ₹2,100.

Additional Information

Ratio and Proportion

If aA = bB, then the ratio A : B is equal to b : a. This helps in converting multi-variable equations into single-variable unit-based problems.

Unitary Method

It involves finding the value of a single unit and then multiplying it by the required number of units to find the final total value.

Linear Equations

Systems like a₁x + b₁y = c₁ can be solved using substitution, elimination, or cross-multiplication methods.

Shortcut Trick

Net percentage change = −12 + 20 + [(−12 × 20) ÷ 100]

Net percentage change = 8 − 2.4 = 5.6% increase

New Price = 8000 × (105.6 ÷ 100) = 80 × 105.6 = 8448

∴ The correct answer is ₹8448.

Alternate Method

Given: Original Price = ₹8,000, First change = 12% decrease, Second change = 20% increase.

⇒ Price after 12% decrease = 8000 − (12% of 8000)

⇒ Price after 12% decrease = 8000 − 960 = ₹7,040

⇒ Price after 20% increase = 7040 + (20% of 7040)

⇒ Price after 20% increase = 7040 + 1408 = ₹8,448

∴ The correct answer is ₹8448.

Additional Information

Successive Percentage Change

If a value is changed by a% and then by b%, the effective net change is [a + b + (ab/100)]%.

Multiplying Factor Method

Final Value = Initial Value × (1 ± r₁/100) × (1 ± r₂/100), where r is the rate of increase/decrease.

Percentage Base Change

When a price decreases by x% and then increases by y%, the base for the second change is the result of the first change.

The given code language is:

Book is common in both the code, and qr is common in both the code.

Thus, 'book' is coded as 'qr'.

Hence, the correct answer is "Option 2".

The Correct answer is Italy.

Key Points

• The Asian Development Bank (ADB) is a regional development bank established to foster economic growth and cooperation in the Asia-Pacific region.
• The 58th Annual Meeting of ADB in 2025 was hosted by Italy, marking a significant step as the meeting was held outside Asia.
• Italy, being a member of ADB, has demonstrated its commitment to global partnerships and sustainable development by hosting this prestigious event.
• During the meeting, India presented its Strategic Action Plan 2025-2029, focusing on long-term goals such as economic development, infrastructure growth, and poverty alleviation.
• The meeting serves as a forum for member countries to discuss important regional issues, financial strategies, and collaborative projects.
• Italy's hosting of this event reflects its active participation in international economic policies despite being geographically outside the Asia-Pacific region.
• This meeting also highlighted Italy's efforts to strengthen ties with Asian nations and contribute to global economic stability.

Additional Information

• China
• China is one of the founding members of ADB and a major contributor to its funding.
• China has hosted multiple international events and conferences but did not host the 58th Annual Meeting of ADB in 2025.
• The country is known for its significant role in regional development and its Belt and Road Initiative.
• Japan
• Japan is a key member of ADB and one of its largest contributors.
• The headquarters of ADB is located in Manila, Philippines, but Japan has been instrumental in shaping ADB’s policies and projects since its inception.
• Although Japan regularly participates in ADB meetings, it was not the host for the 2025 event.
• India
• India is a founding member of ADB and actively engages in its developmental initiatives.
• India’s Strategic Action Plan 2025-2029 was discussed during the meeting, focusing on key areas like infrastructure and sustainable growth.
• Despite its strong involvement, India was not the host for the 58th Annual Meeting in 2025.

Shortcut Trick

For a number to be divisible by 38, it must be divisible by its factors 2 and 19.

Checking options for divisibility by 2: (1) 2620, (3) 1938 are even; (2) 2423, (4) 1495 are odd and eliminated.

Check 1938 for 19: 1900 + 38 = (19 × 100) + (19 × 2) = 19 × 102. It is divisible.

∴ The correct answer is 1938.

Alternate Method

Given: Divisor = 38

Method: Perform direct division for each option to check for zero remainder.

⇒ Option (1): 2620 ÷ 38 ≈ 68.94 (Not divisible)

⇒ Option (2): 2423 ÷ 38 ≈ 63.76 (Not divisible)

⇒ Option (3): 1938 ÷ 38

⇒ 1938 ÷ 38 = 51 (Remainder = 0)

⇒ Option (4): 1495 ÷ 38 ≈ 39.34 (Not divisible)

∴ The correct answer is 1938.

Additional Information

Divisibility by Composite Numbers

A number is divisible by a composite number if it is divisible by its co-prime factors. For 38, factors are 2 and 19.

Divisibility Rule of 19

Multiply the last digit by 2 and add it to the remaining number. If the result is divisible by 19, the whole number is. Example: 193 + (8 × 2) = 209; 20 + (9 × 2) = 38 (Divisible).

Divisibility Rule of 2

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

The Correct answer is Superconducting state.

Key Points

• The Meissner effect is the phenomenon where a material expels magnetic fields when it transitions into the superconducting state.
• This effect is a defining characteristic of superconductors and demonstrates their ability to exhibit perfect diamagnetism.
• In the superconducting state, the material's resistance drops to zero, allowing electric currents to flow without energy loss.
• The effect was discovered in 1933 by Walther Meissner and Robert Ochsenfeld.
• It occurs due to the formation of Cooper pairs, which are paired electrons that move without scattering.
• The Meissner effect is observed below a critical temperature, which varies depending on the type of superconducting material.
• The effect is utilized in technologies such as magnetic levitation and highly efficient electrical systems.
• Superconductors are categorized into two types: Type I and Type II, both exhibiting the Meissner effect but with different behaviors in external magnetic fields.

Additional Information

• Paramagnetic state
• In the paramagnetic state, materials are weakly attracted to external magnetic fields due to the alignment of magnetic moments.
• Unlike the superconducting state, paramagnetic materials do not exhibit zero resistance or expulsion of magnetic fields.
• Examples of paramagnetic materials include aluminum, platinum, and magnesium.
• Ferromagnetic state
• In the ferromagnetic state, materials exhibit strong attraction to magnetic fields and retain their magnetization even after the external field is removed.
• Examples include iron, nickel, and cobalt.
• Ferromagnetic materials are used in applications like electric motors, transformers, and permanent magnets.
• Insulating state
• In the insulating state, materials do not conduct electricity due to the absence of free electrons or charge carriers.
• Common examples include rubber, glass, and ceramics.
• Insulators are widely used in electrical wiring and circuit components to prevent current leakage.

Shortcut Trick

Monthly Savings = 11,000 − (4,000 + 1,500) = ₹5,500.

Total months in a year = 12.

Birthday month savings spent = 1 month.

Total Savings in a year = 5,500 × (12 − 1) = 5,500 × 11 = ₹60,500.

∴ The correct answer is ₹60,500.

Alternate Method

Given:

Monthly salary = ₹11,000

Expenditure on Rent = ₹4,000

Expenditure on Bills = ₹1,500

Calculations:

⇒ Total monthly expenditure = 4,000 + 1,500 = ₹5,500

⇒ Monthly savings = 11,000 − 5,500 = ₹5,500

⇒ Annual savings (without birthday expense) = 5,500 × 12 = ₹66,000

⇒ Amount spent on birthday = Monthly savings of 1 month = ₹5,500

⇒ Final annual savings = 66,000 − 5,500 = ₹60,500

∴ The correct answer is ₹60,500.

Additional Information

Income, Expenditure and Savings

The basic relationship is Income = Expenditure + Savings. Any change in two variables affects the third proportionally.

Percentage Savings

Savings % = (Savings ÷ Total Income) × 100. This is useful for comparing financial habits across different income levels.

Annualization

To convert monthly figures to annual, multiply by 12. If a specific one-time expense occurs, subtract it from the total annual calculation.

The Correct answer is Himadri.

Key Points

• The Himadri, also known as the Greater Himalayas, is the northernmost range of the Himalayan mountain system.
• It contains the loftiest peaks, including the world’s highest peak, Mount Everest (8,848 meters), and several other towering peaks like K2, Kanchenjunga, Nanga Parbat, and Annapurna.
• This range is characterized by its permanent snow cover and is home to some of the largest glaciers, such as the Siachen Glacier and the Gangotri Glacier.
• The Himadri range spans across several countries, including India, Nepal, Bhutan, Pakistan, and China (Tibet).
• The region is geologically young, formed due to the collision between the Indian Plate and the Eurasian Plate.
• It is a significant source of major rivers like the Ganges, Yamuna, Indus, Brahmaputra, and their tributaries.
• The Himadri range plays a crucial role in influencing the climate and weather patterns in South Asia by blocking cold winds and trapping the monsoon rains.
• The region is sparsely populated due to its extreme climatic conditions, high altitude, and rugged terrain.
• The Himadri serves as a hotspot for mountaineering, trekking, and adventure tourism, attracting enthusiasts from across the globe.

Additional Information

• Shiwalik Range
• The Shiwalik Range, also known as the Outer Himalayas, is the southernmost range of the Himalayas.
• It is characterized by low-altitude hills (600-1,200 meters) and is known for its fragile geology.
• This range is primarily composed of sedimentary rocks, making it prone to erosion and landslides.
• It serves as a transition zone between the plains of northern India and the mountainous terrain of the Himalayas.
• Himachal Himalaya
• The Himachal Himalaya, also known as the Lesser Himalayas, lies between the Shiwalik and Himadri ranges.
• This range includes medium-altitude peaks (3,700–4,500 meters) and is rich in vegetation and biodiversity.
• It is home to popular hill stations like Shimla, Manali, Mussoorie, and Nainital.
• The region is known for its agricultural activities, particularly the cultivation of apples and other fruits.
• Purvachal Hills
• The Purvachal Hills are located in the northeastern part of India and are not part of the Himalayan system.
• They include ranges like the Patkai, Naga, Khasi, Jaintia, and Mizo Hills.
• This region is characterized by low-altitude hills and dense forests, making it rich in biodiversity.
• The Purvachal Hills are known for their distinct cultural identity and indigenous tribal communities.

The Correct answer is Australia.

Key Points

• Australia holds federal elections to elect members of its Parliament, which consists of the House of Representatives and the Senate.
• The election date is determined by the Governor-General on the advice of the Prime Minister. In this case, the election was held on 3 May 2025.
• The federal election is conducted by the Australian Electoral Commission (AEC), which ensures the process adheres to democratic standards.
• Australia operates under a compulsory voting system, meaning all eligible citizens are required to vote in federal elections.
• The electoral system used for the House of Representatives is the preferential voting system, while the Senate uses a proportional representation system.
• The elected members of the House of Representatives serve for a term of three years, and the Senate members serve for a term of six years, with half of the Senate seats up for election every three years.
• Australia's federal elections play a crucial role in shaping the country’s governance, as they determine the composition of the government and opposition.

Additional Information

• Canada
• Canada holds federal elections typically every four years, but the actual timing depends on the dissolution of Parliament.
• Canada operates under a parliamentary system with a bicameral legislature consisting of the House of Commons and the Senate.
• The elections are governed by the Canada Elections Act and conducted by Elections Canada.
• New Zealand
• New Zealand has a unicameral parliamentary system, with elections held every three years.
• Elections in New Zealand use the Mixed Member Proportional (MMP) system, combining both electorate and party votes.
• The elections are managed by the Electoral Commission.
• United Kingdom
• The United Kingdom holds general elections typically every five years to elect members of the House of Commons.
• The UK operates under a first-past-the-post electoral system, where the candidate with the most votes in each constituency wins.
• Elections in the UK are managed by the Electoral Commission and overseen by local returning officers.

Given:

: OLR :: PMS : %

Option 1) # = MKI, % = NHU

Option 2) # = JGM, % = URX

 

Option 3) # = LKP, % = FGH

 

Option 4) # = KLM, % = NHY

 

Based on the analysis, only Option 2 maintains a consistent pattern across both pairs.

Hence, the correct answer is "Option 2".

The Correct answer is Article 39A.

Key Points

• Article 39A of the Indian Constitution explicitly provides for free legal aid to the poor and weaker sections of society.
• This Article was added by the 42nd Amendment Act of 1976, which emphasized the need for equal justice and provided a directive to the state to ensure that justice is not denied to any citizen due to economic or other disabilities.
• The provision aims to promote justice on the basis of equal opportunity and ensures that the legal system operates efficiently for all citizens, regardless of their financial status.
• Free legal aid under this Article is a part of the Directive Principles of State Policy (DPSP), which guide the government in framing laws and policies to establish a welfare state.
• The responsibility to provide free legal aid is administered by institutions such as the National Legal Services Authority (NALSA) and respective State Legal Services Authorities.
• It reflects the constitutional vision of ensuring social justice and removing barriers to accessing the legal system for marginalized groups.

Additional Information

• Article 21
• Article 21 guarantees the right to life and personal liberty. It states that no person shall be deprived of their life or personal liberty except according to the procedure established by law.
• This Article has been interpreted widely by the judiciary to include various rights such as the right to privacy, right to health, and right to a clean environment.
• While Article 21 indirectly supports access to justice, it does not specifically provide for free legal aid.
• Article 32
• Article 32 provides the right to constitutional remedies, allowing individuals to move the Supreme Court for the enforcement of their fundamental rights.
• It is often referred to as the "heart and soul of the Constitution" as described by Dr. B.R. Ambedkar.
• This Article empowers the Supreme Court to issue writs such as habeas corpus, mandamus, prohibition, quo warranto, and certiorari for the enforcement of fundamental rights.
• Article 44
• Article 44 falls under the Directive Principles of State Policy (DPSP) and directs the state to strive for a Uniform Civil Code (UCC) throughout the country.
• The UCC aims to replace personal laws based on the scriptures and customs of each major religious community with a common set governing every citizen.
• It is not related to the provision of free legal aid.

The logic followed here is:

Logic: The second number is obtained by dividing the first number by 10 and then subtracting 1 from the result.

i.e., 2nd number = (1st number ÷ 10) - 1

Let's verify this logic with the given pairs:

For (50, 4):

→ 1st number = 50

→ Check 2nd number: (50 ÷ 10) - 1 = 5 - 1 = 4

→ The given 2nd number is 4. The logic holds for the first pair.

For (80, 7):

→ 1st number = 80

→ Check 2nd number: (80 ÷ 10) - 1 = 8 - 1 = 7

→ The given 2nd number is 7. The logic holds for the second pair.

Now, let's apply this logic to the given options:

Option 1) (90, 11)

→ 1st number = 90

→ Check 2nd number: (90 ÷ 10) - 1 = 9 - 1 = 8

→ The given 2nd number is 11. Since 8 ≠ 11, this option does NOT follow the logic.

Option 2) (60, 6)

→ 1st number = 60

→ Check 2nd number: (60 ÷ 10) - 1 = 6 - 1 = 5

→ The given 2nd number is 6. Since 5 ≠ 6, this option does NOT follow the logic.

Option 3) (70, 6)

→ 1st number = 70

→ Check 2nd number: (70 ÷ 10) - 1 = 7 - 1 = 6

→ The given 2nd number is 6. This option follows the logic.

Option 4) (100, 11)

→ 1st number = 100

→ Check 2nd number: (100 ÷ 10) - 1 = 10 - 1 = 9

→ The given 2nd number is 11. Since 9 ≠ 11, this option does NOT follow the logic.

Hence, the correct answer is "Option 3".

The Correct answer is Mahaparinirvan Diwas.

Key Points

• Mahaparinirvan Diwas is observed on 6th December every year to honor the contributions of Dr. B.R. Ambedkar, the architect of the Indian Constitution, towards social justice, equality, and empowerment.
• The term Mahaparinirvan signifies the attainment of ultimate liberation or salvation, which is a Buddhist concept.
• Dr. Ambedkar, a staunch advocate of Dalit rights, passed away on 6th December 1956, and the day has been observed as Mahaparinirvan Diwas since then.
• Dr. Ambedkar was instrumental in combating social discrimination, particularly towards the marginalized sections of society.
• On this day, people across India pay homage to Dr. Ambedkar by visiting his memorial at Chaitya Bhoomi in Mumbai.
• Dr. Ambedkar's work in the fields of law, economics, and social reform continues to inspire millions of people worldwide.
• He was awarded the Bharat Ratna, India’s highest civilian honor, posthumously in 1990.

Additional Information

• Constitution Awareness Day
• Constitution Awareness Day is celebrated on 26th November, the day the Indian Constitution was adopted in 1949.
• The day is also referred to as Constitution Day or Samvidhan Divas.
• It is observed to spread awareness about the importance of the Indian Constitution and its role in ensuring democracy and justice.
• National Equality Day
• While the term National Equality Day is significant, it is not officially recognized or associated with Dr. Ambedkar's contributions.
• The concept focuses on promoting equal rights and opportunities for all citizens.
• Ambedkar Smriti Diwas
• While it may sound relevant, Ambedkar Smriti Diwas is not an officially recognized term for the day honoring Dr. Ambedkar.
• The official day for commemorating Dr. Ambedkar’s contributions is Mahaparinirvan Diwas.

Shortcut Trick

Volume in m³ = 70,000 ÷ 1,000 = 70 m³

Breadth = Volume ÷ (Length × Depth)

Breadth = 70 ÷ (4 × 10) = 70 ÷ 40 = 1.75 m

∴ The correct answer is 1.75 m.

Alternate Method

Given:

Capacity of tank = 70,000 litres

Length (l) = 4 m

Depth (h) = 10 m

Formula Used:

1 m³ = 1,000 litres

Volume of a cuboid = Length × Breadth × Height

Calculations:

⇒ Volume in cubic meters = 70,000 ÷ 1,000 = 70 m³

⇒ Volume = l × b × h

⇒ 70 = 4 × b × 10

⇒ 70 = 40 × b

⇒ b = 70 ÷ 40

⇒ b = 1.75 m

∴ The correct answer is 1.75 m.

Additional Information

Volume of Cuboid

The space occupied by a three-dimensional rectangular object is given by Volume = Length × Breadth × Height.

Unit Conversions

1 m³ = 1,000 litres and 1 litre = 1,000 cm³.

Surface Area of Cuboid

Total Surface Area = 2(lb + bh + hl) and Lateral Surface Area = 2h(l + b).

Given: A, B, C, D, E and F live on six different floors of the same building, numbered 1 to 6 from bottom to top.

E lives on a floor which is a prime number.

The prime numbered floors are 2, 3, and 5.

So, E can live on Floor 2, Floor 3, or Floor 5.

The product of floors on which E and A live is 8.

If E is on Floor 2, then A must be on Floor 4 (2 * 4 = 8).

If E is on Floor 3, then A would have to be on Floor 8/3, which is not possible.

If E is on Floor 5, then A would have to be on Floor 8/5, which is not possible.

Therefore, E must live on Floor 2 and A must live on Floor 4.

C lives immediately above F.

The sum of floors on which A and B live is 7.

We know A lives on Floor 4. So, 4 + B's Floor = 7. This means B's Floor = 3.

So, B lives on Floor 3.

The only remaining person is D, and the only remaining floor is Floor 1.

So, D lives on Floor 1.

Final Arrangement:

C lives on Floor 6.

E lives on Floor 2.

There are 3 people (F, A, B) living between C and E.

Hence, the correct answer is "Option 2".

Here is the alphabetical place value for each letter:

The logic followed in this pattern is a series of alphabetical shifts for each letter position: +3, -3, +2, -2.

For 'LQRU' related to 'ONTS'

For 'RKVQ' related to 'UHXO':

The consistent pattern observed is +3, -3, +2, -2.

Applying the same logic to 'XEZM':

Thus, XEZM is related to ABBK.

Hence, the correct answer is "Option 1".

Shortcut Trick

Savings = 40% → Expenditure = 100% − 40% = 60%.

60% units = ₹480

1% unit = 480 ÷ 60 = 8

100% (Income) = 8 × 100 = ₹800.

∴ The correct answer is ₹800.

Alternate Method

Given:

Savings = 40% of Income

Expenditure = ₹480

Formula: Income = Expenditure + Savings

⇒ Let total Income be ₹I.

⇒ Savings = 0.40 × I

⇒ Expenditure = I − 0.40I = 0.60I

⇒ 0.60 × I = 480

⇒ I = 480 ÷ 0.60

⇒ I = 48000 ÷ 60

⇒ I = 800

∴ The correct answer is ₹800.

Additional Information

Income-Expenditure Relation

Total Income is always the sum of Expenditure and Savings (Income = E + S).

Percentage Base

In such problems, the Income is always treated as the 100% base for calculations.

Savings Ratio

If savings % is S, then expenditure % is (100 − S). Ratio of S : E = Savings % : (100 − Savings %).

Shortcut Trick

Since y varies directly as (x + 3), the ratio y / (x + 3) remains constant.

Ratio 1 = 8 / (1 + 3) = 8 / 4 = 2.

For x = 2, y = 2 × (2 + 3) = 2 × 5 = 10.

∴ The correct answer is 10.

Alternate Method

Given: y ∝ (x + 3), y = 8 when x = 1.

Formula Used: y = k(x + 3), where k is the constant of proportionality.

⇒ 8 = k(1 + 3)

⇒ 8 = 4k

⇒ k = 2

⇒ Now, for x = 2:

⇒ y = 2(2 + 3)

⇒ y = 2 × 5

⇒ y = 10

∴ The correct answer is 10.

Additional Information

Direct Variation

When one quantity increases as the other increases, the relationship is y = kx. The ratio y/x is always constant.

Inverse Variation

When one quantity increases as the other decreases, the relationship is y = k/x. The product x × y is always constant.

Proportionality Constant

The value 'k' represents the constant rate of change between the dependent and independent variables.

Shortcut Trick

Efficiency ratio M : W ⇒ 2M = 9W ⇒ M/W = 9/2.

Total Work = 2 × 9 × 14 = 252 units.

Work done by 2 men in 9 days = 2 × 9 × 9 = 162 units.

Remaining Work = 252 − 162 = 90 units.

Women required (n) × Efficiency (2) × Days (9) = 90 ⇒ n = 90 ÷ 18 = 5.

∴ The correct answer is 5 women.

Alternate Method

Given: 2 Men (M) = 9 Women (W) can complete work in 14 days.

⇒ Efficiency of 1 Man = 18 ÷ 2 = 9 units/day.

⇒ Efficiency of 1 Woman = 18 ÷ 9 = 2 units/day.

⇒ Work done by 2 men in 9 days = (2 × 9) × 9 = 162 units.

⇒ Remaining work = 252 − 162 = 90 units.

⇒ Time allowed for remaining work = 9 days.

⇒ Required efficiency = 90 ÷ 9 = 10 units/day.

⇒ Number of women = Required efficiency ÷ Efficiency of 1 woman.

⇒ Number of women = 10 ÷ 2 = 5.

∴ The correct answer is 5 women.

Additional Information

The 'OR' Concept

When M₁ men OR W₁ women can do a job, equate their total work capacities: M₁ × Days = W₁ × Days to find the efficiency ratio.

Work-Efficiency Formula

Total Work = Efficiency × Time. If work is constant, Efficiency is inversely proportional to Time.

M-D-H Rule

For different groups, use (M₁×D₁×H₁)/W₁ = (M₂×D₂×H₂)/W₂ where M is persons, D is days, H is hours, and W is work.

The Correct answer is Kerala and Assam.

Key Points

• Plantation agriculture is a form of commercial farming where crops are grown for profit.
• In India, plantation agriculture is primarily concentrated in the regions of Kerala and Assam due to their suitable climatic and geographical conditions.
• Kerala is known for the cultivation of crops like rubber, tea, coffee, spices, and coconut, which require a tropical climate and abundant rainfall.
• Assam is globally famous for its tea plantations. The state has a humid subtropical climate with heavy rainfall, making it ideal for tea cultivation.
• Plantation agriculture in these areas contributes significantly to the export economy of India.
• This type of agriculture often involves large-scale monoculture practices and requires a large labor force.
• In Kerala and Assam, plantation agriculture also supports industries like tea processing, rubber production, and spice export.

Additional Information

• Odisha and Chhattisgarh
• These states are not major regions for plantation agriculture but are known for rice cultivation due to their fertile soils and adequate water supply.
• Odisha also grows crops like pulses, oilseeds, and sugarcane, while Chhattisgarh is referred to as the "Rice Bowl of India".
• Rajasthan and Gujarat
• These states are characterized by arid and semi-arid climates, which are unsuitable for plantation agriculture.
• Major crops in these regions include millets, cotton, groundnuts, and oilseeds.
• Rajasthan is known for its dryland farming, while Gujarat is a leading producer of cotton and groundnuts.
• Punjab and Haryana
• These states are the center of intensive subsistence farming and are part of the Green Revolution in India.
• The primary crops grown in this region are wheat, rice, and sugarcane, which are staples of India's food production.
• The climatic and soil conditions in Punjab and Haryana are more suited for cereal and cash crops than plantation crops.

The logic followed here is based on the formula for finding the total number of items in a row/class when the rank of one item from both ends is known.

Given:

• Vijay's rank from the top = 34th
• Vijay's rank from the bottom = 11th

The formula for the total number of students in the class is:

Total number of students = (Rank from Top) + (Rank from Bottom) - 1

Total number of students = 34 + 11 - 1

Total number of students = 45 - 1

Total number of students = 44

Hence, the correct answer is "Option 3".

Decoding symbols:

Given: M + N ÷ O – P × Q

Let's break down the expression step by step:

M + N → M is the mother of N.

N ÷ O → N is the father of O.

O – P → O is the brother of P.

P × Q → P is the wife of Q.

Now, let's trace the relationship from M to Q:

Therefore, M is the Wife's father's mother of Q.

Hence, the correct answer is "Option 2".

Shortcut Trick

Volume of sphere = Volume of cylindrical wire

(4/3) × π × R³ = π × r² × L

(4/3) × 21 × 21 × 21 = 0.3 × 0.3 × L (all in cm)

L = (4 × 7 × 21 × 21) ÷ 0.09 = 137200 cm = 1372 m

∴ The correct answer is 1372 m.

Alternate Method

Given:

Diameter of sphere (D) = 42 cm ⇒ Radius (R) = 21 cm

Diameter of wire (d) = 0.6 cm ⇒ Radius (r) = 0.3 cm

Formula Used:

Volume of sphere = (4/3) × π × R³

Volume of cylinder (wire) = π × r² × h (where h is the length L)

Calculations:

⇒ Volume of sphere = Volume of wire

⇒ (4/3) × π × (21)³ = π × (0.3)² × L

⇒ (4/3) × 21 × 21 × 21 = 0.09 × L

⇒ 4 × 7 × 441 = 0.09 × L

⇒ 12348 = 0.09 × L

⇒ L = 12348 ÷ 0.09 = 137200 cm

⇒ L (in metre) = 137200 ÷ 100 = 1372 m

∴ The correct answer is 1372 m.

Additional Information

Volume Invariance

When a solid is melted and recast into a new shape, the total volume remains constant, provided there is no wastage.

Cylinder Properties

For a wire (cylinder), the curved surface area is 2πrh and the total surface area is 2πr(h + r).

Unit Conversion

1 metre = 100 centimetres. Always ensure all dimensions are in the same system before calculation.

The Correct answer is Quick Access.

Key Points

• Quick Access is a feature in Windows File Explorer that allows users to pin and access their most frequently used folders and files easily.
• It provides a convenient location for users to view recently accessed files and folders, promoting efficiency in navigating the system.
• This feature is automatically updated based on user activity, displaying the files and folders that are most relevant to the user at a given time.
• Users can also manually pin folders to the Quick Access section for quick retrieval.
• It enhances productivity by eliminating the need to search for frequently used files and directories across the file system.
• Quick Access is located at the top of the navigation pane in File Explorer in Windows 10 and Windows 11.
• It is particularly useful for professionals and students managing a large number of files and folders daily.

Additional Information

• Task Bar
• The Task Bar is a graphical interface element in Windows that displays running applications, system notifications, and shortcuts to certain programs.
• It is located at the bottom of the desktop by default and contains the Start menu, search bar, and system tray.
• Its primary function is to manage open programs and provide quick access to pinned applications, not folders.
• File Explorer
• File Explorer is the primary file management system in Windows, allowing users to browse, manage, and organize files and folders.
• It provides access to system drives, external drives, and network locations.
• While it contains the Quick Access feature, File Explorer itself is not specifically designed for creating shortcuts to frequently used folders.
• Libraries
• Libraries are a feature in Windows that allow users to organize content from multiple folders into a single virtual collection.
• They are best suited for categorizing files by type, such as documents, music, pictures, and videos.
• However, Libraries do not serve as a shortcut tool for quick access to frequently used folders.

The Correct answer is Hard Disk Drive (HDD).

Key Points

• The Hard Disk Drive (HDD) is a storage device that is not part of the Central Processing Unit (CPU).
• The CPU consists of components like the Control Unit (CU), Arithmetic Logic Unit (ALU), and Cache Memory, which work together to process data and execute instructions.
• Unlike the CPU, the HDD is primarily used for long-term data storage and does not perform data processing or execution of instructions.
• The HDD is considered an external storage device connected to the computer system to store files, programs, and operating systems.
• HDDs are slower compared to RAM or Cache Memory when it comes to accessing data, as they are designed for mass storage rather than quick access.
• Modern computers often use Solid State Drives (SSD) alongside or in place of HDDs due to their faster data access speeds.

Additional Information

• Cache Memory
• Cache Memory is a small-sized, high-speed memory located within the CPU or very close to it.
• It stores frequently accessed data and instructions to improve the processing speed of the CPU.
• Cache memory is faster than RAM and is used to reduce the time taken to access data from the main memory.
• Control Unit (CU)
• The Control Unit is one of the main components of the CPU and is responsible for directing the flow of data and instructions.
• It interprets program instructions and controls the operation of the CPU's other components, such as the ALU and memory.
• The CU is crucial for the execution of programs and ensures proper coordination between various parts of the computer.
• Arithmetic Logic Unit (ALU)
• The Arithmetic Logic Unit performs all the arithmetic (e.g., addition, subtraction) and logical operations (e.g., comparisons) required for processing data.
• The ALU is integral to the CPU and works closely with the Control Unit to execute instructions.
• It is a fundamental component for tasks that involve mathematical computations and decision-making processes.